Convention. composition [kostecki2011introduction, 1.1] [tt-003X]

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In literatures, composition of arrows in a category is most frequently denoted \(\circ \) or just by juxtaposition, i.e. for the diagram

But this is the opposite of the order of arrows in the diagram, so arguably a more natural way could be to denote the above as \(f ; g\) [kostecki2011introduction, 1.1], or as \(f \mathbin {⨟} g\) [fong2018seven, 3.6], or as \(f \mathbin {\bullet } g\) [nakahira2023diagrammatic, sec. 1.1].

We use \(f \mathbin {\bullet } g\) throughout this note, so it can always be understood as \(\xrightarrow {f}\xrightarrow {g}\). This way saves mental energy when reading commuting diagrams, pasting diagrams and string diagrams which we employ heavily.